The blue coloration of Morpho butterflies has anomalously low angular dependence despite the production of color with a selected wavelength based on an interference effect. A key to the mechanism of the specific Morpho-color was suggested to be the randomness of its scale. Using finite-difference time-domain (FDTD) analysis, the role of different kinds of randomness in the structure of the Morph butterfly's scale was investigated, which was impossible by conventional analytical calculations. The results revealed that incoherence in the incident light plays an essential role, which cannot be realized only by structural randomness. On the other hand, the lateral and vertical randomness, and the number of random components were found each to have an independent role to realize the specific Morpho-color preventing the sharp reflective angular dependence. The direction obtained by the numerical simulations to analyze optically complex random structures will serve not only to understand the scientific principles, but also to design the optical properties of artificial materials.